BCI-algebras with Condition (S) and their Properties

Sun, Tao; Zhao, Junjie; Liang, Xiquan

doi:10.2478/v10037-008-0010-6

Abstract

In this article we will first investigate the elementary properties of BCI-algebras with condition (S), see [8]. And then we will discuss the three classes of algebras: commutative, positive-implicative and implicative BCK-algebras with condition (S).

MML identifier: BCIALG 4, version: 7.8.09 4.97.1001

References

[1] Grzegorz Bancerek. Curried and uncurried functions. Formalized Mathematics, 1(3):537-541, 1990.
Search in Google Scholar
[2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
Search in Google Scholar
[3] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
Search in Google Scholar
[4] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
Search in Google Scholar
[5] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
Search in Google Scholar
[6] Yuzhong Ding. Several classes of BCI-algebras and their properties. Formalized Mathematics, 15(1):1-9, 2007.10.2478/v10037-007-0001-z
Search in Google Scholar
[7] Yuzhong Ding and Zhiyong Pang. Congruences and quotient algebras of BCI-algebras. Formalized Mathematics, 15(4):175-180, 2007.10.2478/v10037-007-0021-8
Search in Google Scholar
[8] Jie Meng and YoungLin Liu. An Introduction to BCI-algebras. Shaanxi Scientific and Technological Press, 2001.
Search in Google Scholar
[9] Andrzej Trybulec. Semilattice operations on finite subsets. Formalized Mathematics, 1(2):369-376, 1990.
Search in Google Scholar
[10] Wojciech A. Trybulec. Binary operations on finite sequences. Formalized Mathematics, 1(5):979-981, 1990.
Search in Google Scholar
[11] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
Search in Google Scholar
[12] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
Search in Google Scholar

BCI-algebras with Condition (S) and their Properties

Abstract

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